On the effectiveness of genetic search in combinatorial optimization

In this paper, we study the e cacy of genetic algorithms in the context of combinatorial optimization. In particular, we isolate the e ects of cross-over, treated as the central component of genetic search. We show that for problems of nontrivial size and di culty, the contribution of cross-over search is marginal, both synergistically when run in conjunction with mutation and selection, or when run with selection alone, the reference point being the search procedure consisting of just mutation and selection. The latter can be viewed as another manifestation of the Metropolis process. Considering the high computational cost of maintaining a population to facilitate cross-over search, its marginal bene t renders genetic search inferior to its singletonpopulation counterpart, the Metropolis process, and by extension, simulated annealing. This is further compounded by the fact that many problems arising in practice may inherently require a large number of state transitions for a near-optimal solution to be found, making genetic search infeasible given the high cost of computing a single iteration in the enlarged state-space. A short version will appear in Proc. 10th ACM Symposium on Applied Computing, Genetic Algorithms and Optimization Track, February, 1995. Supported in part by NSF grant CCR-9204284 0